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Total variation regularization for manifold-valued data.
SIAM J. Imaging Sci. 7, 2226-2257 (2014)
We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These algorithms are based on iterative geodesic averaging which makes them easily applicable to a large class of data manifolds. As an application, we consider denoising images which take their values in a manifold. We apply our algorithms to diffusion tensor images, interferometric SAR images as well as sphere and cylinder valued images. For the class of Cartan-Hadamard manifolds (which includes the data space in diffusion tensor imaging) we show the convergence of the proposed TV minimizing algorithms to a global minimizer.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Diffusion Tensor Imaging ; Manifold-valued Data ; Proximal Point Algorithm ; Total Variation Minimization
ISSN (print) / ISBN 1936-4954
Journal SIAM Journal on Imaging Sciences
Quellenangaben Volume: 7, Issue: 4, Pages: 2226-2257
Publishing Place Philadelphia, Pa.
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)